# Homomorphic Authenticators

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## Abstract

Homomorphic authenticators allow to evaluate functions on *authenticated* data. There exist constructions both in the secret key setting in the form of *homomorphic message authentication codes (MACs)* and in the public key setting in the form of *homomorphic signatures*. These solutions can be used to respectively construct *privately* and *publicly verifiable computing schemes*. There are homomorphic MAC and signature schemes that are not known to allow verification faster than computing the function, e.g. Gennaro and Wichs (Fully homomorphic message authenticators, in *Advances in Cryptology - ASIACRYPT 2013 - 19th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II*, Bengaluru, 1–5 December 2013, pp. 301–320) or Freeman (Improved security for linearly homomorphic signatures: a generic framework, in *Public Key Cryptography - PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings*, Darmstadt, 21–23 May 2012, pp. 697–714), and are therefore not considered in this chapter. In the following, first, we provide the definitions for schemes using homomorphic authenticators and their correctness and security. Then we present privately verifiable computing schemes using MACs, i.e. “Verifiable Delegation of Computation on Outsourced Data” by Backes et al., “Generalized Homomorphic MACs with Efficient Verification” by Zhang and Safavi-Naini, and “Efficiently Verifiable Computation on Encrypted Data” by Fiore et al. Afterwards, we present the publicly verifiable computing schemes using homomorphic signatures, i.e. “Programmable Hash Functions Go Private” by Catalano et al., “Homomorphic Signatures with Efficient Verification for Polynomial Functions” by Catalano et al., and “Algebraic (Trapdoor) One-Way Functions and their Applications” by Catalano et al. Finally, we present an approach by Lai et al., “Verifiable Computation on Outsourced Encrypted Data”, showing how to combine signature based verifiable computing with homomorphic encryption assuring privacy of the data processed.

## Keywords

Signature Scheme Homomorphic Encryption Semantic Security Homomorphic Encryption Scheme Verifiable Computation## References

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